Piecewise polynomials, Minkowski weights, and localization on toric varieties

Katz, Eric; Payne, Sam

doi:10.2140/ant.2008.2.135

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Piecewise polynomials, Minkowski weights, and localization on toric varieties

Eric Katz and Sam Payne

Vol. 2 (2008), No. 2, 135–155

DOI: 10.2140/ant.2008.2.135

Abstract

We use localization to describe the restriction map from equivariant Chow cohomology to ordinary Chow cohomology for complete toric varieties in terms of piecewise polynomial functions and Minkowski weights. We compute examples showing that this map is not surjective in general, and that its kernel is not always generated in degree one. We prove a localization formula for mixed volumes of lattice polytopes and, more generally, a Bott residue formula for toric vector bundles.

Keywords

toric variety, localization, tropical geometry, piecewise polynomial, Minkowski weight

Mathematical Subject Classification 2000

Primary: 14M25

Secondary: 14C17, 52B20

Milestones

Received: 2 April 2007

Revised: 22 October 2007

Accepted: 20 November 2007

Published: 15 March 2008

Authors

Eric Katz
Department of Mathematics University of Texas Austin, TX 78712 United States

Sam Payne
Department of Mathematics, Bldg 380 Stanford University Stanford, CA 94305 United States

Vol. 2, No. 2, 2008